A student in the AI course creates an alert system to detect possible late clients in credit operations. A bank does intensive testing of the system based on the records of its customer portfolio and determines that if the person is late, the system is correct in classifying them as such 95% of the time and that if the person is punctual, the system fails. by classifying her as unpunctual 3% of the time. Bank records reveal that 10% of customers default, while 90% do not. If a customer, selected at random, is classified as late by the system, what is the probability that he or she really is?

This problem can be solved using Bayes' theorem. Let's define some terms to make the calculation easier: Let A be the event that a customer is truly late. Let B be the event that the system classifies a customer as late. We want to find the conditional probability P(A | B), which is the probability that a customer is truly late given that the system classifies them as late. We are given the following probabilities: P(A) = Probability that a customer is truly late = 10% = 0.10 P(not A) = Probability that a customer is truly punctual = 90% = 0.90 P(B | A) = Probability that the system classifies a truly late customer as late = 95% = 0.95 P(B | not A) = Probability that the system classifies a truly punctual customer as late = 3% = 0.03 We can calculate P(B) using the law of total probability: P(B) = P(B | A) * P(A) + P(B | not A) * P(not A) P(B) = (0.95 * 0.10) + (0.03 * 0.90) P(B) = 0.095 + 0.027 P(B) = 0.122 Now, we can use Bayes' theorem to find P(A | B): P(A | B) = (P(B | A) * P(A)) / P(B) P(A | B) = (0.95 * 0.10) / 0.122 P(A | B) ≈ 0.776 So, if a customer is classified as late by the system, the probability that they are truly late is approximately 77.6%.